RECORD OF EMAIL EXCHANGES WITH MELVYN LAFITTE 1995 - 2007 N. J. A. Sloane April 7, 2017 This concerns the three sequences which are now A000360, A000361, A000876 (the three sequence #1, #2, #3 mentioned here) Since the articles by Mel Lafitte cited in A000360 seem to be unobtainable (even in the EPFL library at Lausanne) and Mel Lafitte cannot be reached, I am making these emails public. This txt file will be attached to A000360, along with the latex source (also given below) and a pdf file of the output. Also the gif file that he mentiones. Unfortunately I have not been able to locate the attachments that he sent along with one of these emails, from 22 years ago. From masg2.epfl.ch!lafitte Tue Apr 25 10:14:30 0600 1995 From: Melvyn Lafitte Date: Tue, 25 Apr 1995 10:14:30 -0600 To: njas@research.att.com Subject: New Sequence Attn:NJA Sloane Hello ! I submitted the following sequence to your "superseeker": 1 0 1 1 1 1 2 0 2 2 2 1 3 1 2 1 2 2 4 1 4 3 3 1 4 2 4 2 ... It is not in your table, nor those it recognize it. I consider it to be a very interesting integer sequence. I obtained it using a special scheme on a self-replicating tiling, tiling I came upon four years ago. My email adress is:melvyn.lafitte@dma.epfl.ch I thank you in advance for considering to insert this sequence in your table. Continue this great useful work. MJL. Melvyn Jeremie Lafitte | Departement de Mathematiques dit Mandelvyn | Ecole Polytechnique Federale de Lausanne Email: melvyn.lafitte@dma.epfl.ch | ETH-Lausanne (Sister of ETH-Zurich) ______________________________________________________________________________ "If you really believe in quantum mechanics, then you can't take it seriously." Bob Wald. ______________________________________________________________________________ From njas Sun Apr 30 13:46 EDT 1995 To: melvyn.lafitte@dma.epfl.ch Cc: njas please remember to send me the explanation of this sequence! 1 0 1 1 1 1 2 0 2 2 2 1 3 1 2 1 2 2 4 1 4 3 3 1 4 2 4 2 and some more terms! best regards neil sloane From masg2.epfl.ch!lafitte Wed May 3 21:25:04 0600 1995 From: Melvyn Lafitte Date: Wed, 3 May 1995 21:25:04 -0600 To: njas@research.att.com Subject: 1 0 1 1 1 1 2 0 2 2 2 1 3 1 2 1 2 2 4 1 4 3 3 1 4 2 4 2 %PLEASE CONSIDER THE FOLLOWING TEXT AS AMSLATEX INPUT: \documentstyle[amscd,amssymb,verbatim,epsf]{amsart} \begin{document} Attn: NJA Sloane I'm sorry not to have got back to you before. Like I told you, the sequence is related to a Self-Replicating tile. (I'm sending another message with an uuencoded image of it) The self-replicating tile may be obtained by the following iterated functions system:\\ $ \begin{pmatrix} \xi' \\ \eta' \end{pmatrix} =\frac{1}{2} ( \begin{pmatrix} \xi \\ \eta \end{pmatrix} + \begin{pmatrix} 0 \\ \frac{\sqrt{3}}{2} \end{pmatrix} ) $ \\ $ \begin{pmatrix} \xi' \\ \eta' \end{pmatrix} =\frac{1}{2} ( \begin{pmatrix} \xi \\ \eta \end{pmatrix} + \begin{pmatrix} 0 \\ \frac{\sqrt{3}}{6} \end{pmatrix} ) $ \\ $ \begin{pmatrix} \xi' \\ \eta' \end{pmatrix} =\frac{1}{2} ( \begin{pmatrix} \xi \\ \eta \end{pmatrix} + \begin{pmatrix} \frac{1}{2} \\ 0 \end{pmatrix} ) $ \\ $ \begin{pmatrix} \xi' \\ \eta' \end{pmatrix} =\frac{1}{2} ( \begin{pmatrix} \xi \\ \eta \end{pmatrix} + \begin{pmatrix} -\frac{1}{2} \\ 0 \end{pmatrix} ) $ to the interval $\cal{I}$ \\ It is the attractor of this IFS, a very interesting triangle shaped fractal of non-empty interior and of Hausdorff dimension equal to 2. (and that satisfies the open set condition without allowing a stronger condition)\\ This fractal has been discovered by myself in 1991. I later came to know that Gosper had encountered it at about the same time, that Mandelbrot also encountered an object, formed by the union of copies of this fractal, in 1975 and lately I read an article by C. Bandt exposing facts about self-replicating tiles and giving as example this fractal.\\ At that time, I made a thorough study of this fractal. I've been able to prove 2 very elegant laws of formation (aside from its selfsimilar structure) based on the way it is "filled", indeed this fractal is composed of filled equal triangles . (equal in the sense: by similitude)\\ Now congruent filled triangles can be found on lines perpendicular to a side of the triangle shape of the object (triangle convex hull).\\ As we consider smaller and smaller filled triangles, we get more and more of them on these lines. \\ Well my sequence 1 0 1 1 1 ... results from counting these filled congruent triangles on these lines, and so each term corresponds to a line, to the counting on that line. (Remark that on these lines, are also empty triangles, triangles congruent to the triangles which are filled)\\ Understand that this forms a sequence only because there happens (proved) to be an additional self-similarity given to the object, and that it assures that counts for a certain size of triangles will be the same than for a greater size of triangles, but with more terms (counts) added.\\ I came to prove that this sequence is closely related to the sequence A2487 M0141 N0056, in fact it is a transformation of this sequence by: $new(3 n)=\frac{old(3n)+1}{2}$ \\ $new(3 n + 1)=\frac{old(3 n + 1)-1}{2}$ \\ $new(3 n + 2)=\frac{old(3 n + 2)}{2}$ \\ I did not intend to send you this sequence but another one which also results from this triangle shaped fractal. It is by mistake that I copied this sequence in my message and not that other one. In fact, this sequence I sent you is pretty interesting, even if it is the transformation of another known sequence, because for me it rather is the way those filled triangles are distributed along these lines on this object before being a transformation of that already known sequence. So I can give you 60 terms: 1 0 1 1 1 1 2 0 2 2 2 1 3 1 2 1 2 2 4 1 4 3 3 1 4 2 4 2 3 2 3 0 3 3 4 2 6 3 5 2 5 4 7 2 6 4 4 1 5 3 6 3 6 4 6 1 5 4 5 2 5 2 3 ...\\ Now the intended integer sequence starts by: 1 0 2 1 1 2 5 0 10 6 3 2 18 2 10 ...\\ It is a consideration of the filled and empty triangles on a line as the binary expansion of an integer:0 for empty and 1 for filled: \begin{verbatim} 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 ... \end{verbatim} $\downarrow$\\ 1;0;10;1;001;10;101;0;1010;110;00011;10;10011;010;1010;... It describes these ``fillings'' on these lines much better than the rather incomplete description that the counting of the filled (first sequence) only gives us.\\ I will be sending you about 60 terms in the days coming.\\ There are'nt any references on this sequence. In fact, I plan to finally publish some of my results in the near future. For me this rep-tile (and the sequence related to it), and the study I undertook on it, are only indications of a general and elegant theory concerning ``critical'' cases of self-similarity, theory I started to develop precisely after I met this example. Please consider including these (especially the second one) sequences in your table and continue this very useful work.\\ Best Regards,\\ MJL. PS:Please refer me with the email adress:melvyn.lafitte@@dma.epfl.ch instead of any other non constantly working adress. Thanks. ______________________________________________________________________________ Melvyn Jeremie Lafitte | Departement de Mathematiques dit Mandelvyn | Ecole Polytechnique Federale de Lausanne Email: melvyn.lafitte@dma.epfl.ch | ETH-Lausanne (Sister of ETH-Zurich) ______________________________________________________________________________ Syag LeHochma -- Shtika ( Wisdom is delineated by silence.) ______________________________________________________________________________ From masg32.epfl.ch!lafitte Thu May 11 16:29:44 0600 1995 From: Melvyn Lafitte Date: Thu, 11 May 1995 16:29:44 -0600 To: njas@research.att.com Hello ! I'm sorry you could'nt have my amslatex mail working correctly on a first try. Receiving your mail about these errors, I wrote a second version of this humble note. It is much more understandable and corrects things unclear (like how did I consider the old(n) sequence to be initialized). Now I also dared to go further in what I originally wanted to give you. Because in fact this rep-tile hides supplemental self-similarity (based on ``negation''), than the original structure directly gives, one can consider the sequence 1 0 2 1 1 2 5 0 10 6 ... BUT it is a more proper task to consider the ``essential'' sequence 1 1 0 0 3 3 0 0 1 0 1 1 2 0 7 7 0 2 1 1 0 1 2 ... given in the revised version of this note. I am sorry for giving these little results by ``crumbs'' one at a time, but when I wrote to you concerning the most simply explainable sequence on this rep-tile ( 1 0 1 1 1 1 2 0 2 2 2 1 3 1 ...), I was afraid it was to much to explain in a simple email message where exactly all this was heading. Now here also, I am not going quite far but I sure am thankful to you for taking the time to read this note, quite long for not much. (to explain a simple thing is always so much easier eyes to eyes than on written paper !) SO to resume/review the sequences sent to you: 1.) Counting filled triangles(Transformation of a known sequence): 1 0 1 1 1 1 2 0 2 2 2 1 3 1 2 1 2 2 4 1 4 3 3 1 4 2 4 2 3 2 3 0 3 3 4 2 6 3 5 2 5 4 7 2 6 4 4 1 5 3 6 3 6 4 6 1 5 4 5 2 5 2 3 ... 2.) Coarse binary consideration of the filled and empty triangles: 1 0 2 1 1 2 5 0 10 6 3 2 19 2 10 1 5 10 89 1 170 28 7 2 71 12 170 5 25 10 21 0 42 26 51 10 1251 38 682 6 301 170 5833 3 2730 120 15 2 271 56 ... 3.) ``Essential''(titen) binary consideration of the filled and empty triangles: 1 1 0 0 3 3 0 0 1 0 1 1 2 0 7 7 0 2 1 1 0 1 2 2 3 0 3 6 10 0 13 2 9 3 10 0 15 15 0 10 3 9 2 13 0 10 6 3 0 3 2 2 5 2 25 1 42 12 7 0 7 28 170 1 217 10 37 1 ... I only recommend sequences 1.) and 3.). 3.) is a much better study of what really is taking place here than 2.). But one might as well chose 1.) and 2.) Again thank you for taking time to read this. Continue this useful work. Best Regards, MJL. PS: I just received your mail telling me you succeeded in reading the original note. Well, sorry, now you will have to read this one! Thank you for your interest in this little exotic tile research, I will send you copies of papers on this subject as soon as I get them published. NB: The revised version of the note is sent to you by 2 other email messages. (as uuencoded postscript file and as an uuencoded dvi file in case the postscript file is too printer dependent ...) ______________________________________________________________________________ Melvyn Jeremie Lafitte | Departement de Mathematiques dit Mandelvyn | Ecole Polytechnique Federale de Lausanne Email: melvyn.lafitte@dma.epfl.ch | ETH-Lausanne (Sister of ETH-Zurich) ______________________________________________________________________________ Syag LeHochma -- Shtika ( Wisdom is delineated by silence.) ______________________________________________________________________________ From masg32.epfl.ch!lafitte Tue Aug 29 16:02:53 0600 1995 Received: by rice; Tue Aug 29 10:05 EDT 1995 Received: by research.att.com; Tue Aug 29 10:03 EDT 1995 Received: from masg32.epfl.ch by sicmail.epfl.ch with SMTP (PP) id <26982-0@sicmail.epfl.ch>; Tue, 29 Aug 1995 16:02:54 +0200 From: Melvyn Lafitte Message-Id: <9508291602.ZM7948@dma.epfl.ch> Date: Tue, 29 Aug 1995 16:02:53 -0600 X-Mailer: Z-Mail (3.2.0 26oct94 MediaMail) To: njas@research.att.com Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Status: RO Attn: NJA Sloane Hello, Being absent for weeks, I found a message from J. Shallit. He found one of "my" sequences in your table and so is asking for more explanations. I will give them to him. Wanting to know what he knew from the information in your table, I looked up the sequences and so realised you hadn't received the "second" version of my note. (sent months ago just after you had problems in reading the first version; first version, you finally were able to get compiled by tex) I don't know what happened. Did I mistake your email adress? Did you think it was the same first version ?... Well... It is of no importance ! Mainly 2 things in this note: - a little detail in the expression of newsequence=f(oldsequence). In the first version I used d(-1)=0, d(0)=1, but it is more usual to use d(0)=0, d(1)=1. f is now expressed taking account of this. So for the %F of the first sequence (1 0 1 1 1 1 2 0 2...) write: new(3n+1)=(old(3n+1)+1)/2; new(3n+2)=(old(3n+2)-1)/2; new(3n)=old(3n)/2 instead of what is currently written in the table. - a 3rd sequence, 1 1 0 0 3 3 0 0 1 0 1 1 2 0 7 7 0 2 1 1 0 1 2 2 3 0 3 6 10 0 13 2 9 3 10 0 15 15 0 10 3 9 2 13 0 10 6 3 0 3 2 2 5 2 25 1 42 12 7 0 7 28 170 1 217 10 37 1 ... I didn't send you with the first version, fearing it was too much "rocambolesque" explanations at one time. It is much more profound and accurate in describing what really is happening in the filling of the triangle shaped tiling. The first sequence (1 0 1 1 1 1 2 0 2...) is itself interesting in the relation it has with A2487 but the 3rd sequence takes care to remove all the "redundancies" in what is observed. (For explanations on this sequence, see "second" version of note) Please consider this 3rd sequence. It is to my opinion of much more interest than the 2nd one (1 0 2 1 1 2 5 0 10 6 3 2 19 2 10 ...) you have recorded in your table. Please note also, that in your table this 2nd sequence wasn't copied correctly: there is an `18' recorded instead of the correct `19'. Here are more terms for this 2nd seq. than what is actually recorded: 1 0 2 1 1 2 5 0 10 6 3 2 19 2 10 1 5 10 89 1 170 28 7 2 71 12 170 5 25 10 21 0 42 26 51 10 1251 38 682 6 301 170 5833 3 2730 120 15 2 271 56 ... In accordance, I am sending you a uuencoded version of the PS file containing this second version of my note. I understand you're busy and so excuse myself in having to explain all this little stuff in my message: when I write those papers on the researchs that gave me, among other more consistant things, these sequences, you will receive a copy. Best Regards, Melvyn. ______________________________________________________________________________ Melvyn Jeremie Lafitte | Departement de Mathematiques dit Mandelvyn | Ecole Polytechnique Federale de Lausanne Email: melvyn.lafitte@dma.epfl.ch | ETH-Lausanne (Sister of ETH-Zurich) ______________________________________________________________________________ "If you really believe in quantum mechanics, then you can't take it seriously." Bob Wald. ______________________________________________________________________________ From njas Tue Aug 29 21:27 EDT 1995 Received: by rice; Tue Aug 29 21:27 EDT 1995 From: research!njas Date: Tue, 29 Aug 95 21:27 EDT To: masg32.epfl.ch!lafitte Cc: njas@research.att.com thank you for the message and the compressed file i added the extra terms ( and made that correction) to the second sequence to save time, could you simply send me the third sequence, the new on, in my standard format? following the example of tyhe second sequence, which now reads: %I A0361 %S A0361 1,0,2,1,1,2,5,0,10,6,3,2,19,2,10,1,5,10,89,1,170,28,7,2,71,12 %T A0361 170,5,25,10,21,0,42,26,51,10,1251,38,682,6,301,170,5833,3,2730 %U A0361 120,15,2,271,56 %N A0361 From a self-replicating tiling. %R A0361 %K A0361 nonn %O A0361 0,3 %E A0361 corrected 8/95. %A A0361 Melvyn Jeremie Lafitte then i will be very happy to add it to the table! best regards neil From masg49.epfl.ch!lafitte Wed Aug 30 11:44:09 0600 1995 Received: by rice; Wed Aug 30 05:45 EDT 1995 Received: by research.att.com; Wed Aug 30 05:44 EDT 1995 Received: from masg49.epfl.ch by sicmail.epfl.ch with SMTP (PP) id <20772-0@sicmail.epfl.ch>; Wed, 30 Aug 1995 11:44:09 +0200 From: Melvyn Lafitte Message-Id: <9508301144.ZM7113@dma.epfl.ch> Date: Wed, 30 Aug 1995 11:44:09 -0600 In-Reply-To: njas@research.att.com "" (Aug 29, 9:27pm) References: <199508300128.DAA09102@masg32.epfl.ch> X-Mailer: Z-Mail (3.2.0 26oct94 MediaMail) To: njas@research.att.com Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Status: RO Attn: NJA Sloane Thank you for the message. Here is the 3rd sequence in your standard format: %I A0362 %S A0362 1,1,0,0,3,3,0,0,1,0,1,1,2,0,7,7,0,2,1,1,0,1,2,2,3,0,3,6,10 %T A0362 0,13,2,9,3,10,0,15,15,0,10,3,9,2,13,0,10,6,3,0,3,2,2,5,2,25 %U A0362 1,42,12,7,0,7,28,170,1,217,10,37,1 %N A0362 From a self-replicating tiling. %R A0362 %K A0362 nonn %O A0362 0,5 %A A0362 Melvyn Jeremie Lafitte I did not know what to write at the A???? place, so i've just put A0362. When i'll have more time for this, i will devise a (very ?) short Mathematica program, out of the ones i use now, to calculate this 3rd sequence and will send it to you. Best Regards, Melvyn. ______________________________________________________________________________ Melvyn Jeremie Lafitte | Departement de Mathematiques dit Mandelvyn | Ecole Polytechnique Federale de Lausanne Email: melvyn.lafitte@dma.epfl.ch | ETH-Lausanne (Sister of ETH-Zurich) ______________________________________________________________________________ Rabbi Zoucha d'Anipoly avait pour habitude de repeter: "Zoucha, Quand tu retourneras chez ton Cre-teur, Il ne te demandera pas pourquoi tu n'etais pas Moise ou David mais pourquoi tu n'etais pas Zoucha ! " ______________________________________________________________________________ From masg32.epfl.ch!lafitte Tue Aug 29 16:02:53 0600 1995 Received: by rice; Tue Aug 29 10:05 EDT 1995 Received: by research.att.com; Tue Aug 29 10:03 EDT 1995 Received: from masg32.epfl.ch by sicmail.epfl.ch with SMTP (PP) id <26982-0@sicmail.epfl.ch>; Tue, 29 Aug 1995 16:02:54 +0200 From: Melvyn Lafitte Message-Id: <9508291602.ZM7948@dma.epfl.ch> Date: Tue, 29 Aug 1995 16:02:53 -0600 X-Mailer: Z-Mail (3.2.0 26oct94 MediaMail) To: njas@research.att.com Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Status: RO Attn: NJA Sloane Hello, Being absent for weeks, I found a message from J. Shallit. He found one of "my" sequences in your table and so is asking for more explanations. I will give them to him. Wanting to know what he knew from the information in your table, I looked up the sequences and so realised you hadn't received the "second" version of my note. (sent months ago just after you had problems in reading the first version; first version, you finally were able to get compiled by tex) I don't know what happened. Did I mistake your email adress? Did you think it was the same first version ?... Well... It is of no importance ! Mainly 2 things in this note: - a little detail in the expression of newsequence=f(oldsequence). In the first version I used d(-1)=0, d(0)=1, but it is more usual to use d(0)=0, d(1)=1. f is now expressed taking account of this. So for the %F of the first sequence (1 0 1 1 1 1 2 0 2...) write: new(3n+1)=(old(3n+1)+1)/2; new(3n+2)=(old(3n+2)-1)/2; new(3n)=old(3n)/2 instead of what is currently written in the table. - a 3rd sequence, 1 1 0 0 3 3 0 0 1 0 1 1 2 0 7 7 0 2 1 1 0 1 2 2 3 0 3 6 10 0 13 2 9 3 10 0 15 15 0 10 3 9 2 13 0 10 6 3 0 3 2 2 5 2 25 1 42 12 7 0 7 28 170 1 217 10 37 1 ... I didn't send you with the first version, fearing it was too much "rocambolesque" explanations at one time. It is much more profound and accurate in describing what really is happening in the filling of the triangle shaped tiling. The first sequence (1 0 1 1 1 1 2 0 2...) is itself interesting in the relation it has with A2487 but the 3rd sequence takes care to remove all the "redundancies" in what is observed. (For explanations on this sequence, see "second" version of note) Please consider this 3rd sequence. It is to my opinion of much more interest than the 2nd one (1 0 2 1 1 2 5 0 10 6 3 2 19 2 10 ...) you have recorded in your table. Please note also, that in your table this 2nd sequence wasn't copied correctly: there is an `18' recorded instead of the correct `19'. Here are more terms for this 2nd seq. than what is actually recorded: 1 0 2 1 1 2 5 0 10 6 3 2 19 2 10 1 5 10 89 1 170 28 7 2 71 12 170 5 25 10 21 0 42 26 51 10 1251 38 682 6 301 170 5833 3 2730 120 15 2 271 56 ... In accordance, I am sending you a uuencoded version of the PS file containing this second version of my note. I understand you're busy and so excuse myself in having to explain all this little stuff in my message: when I write those papers on the researchs that gave me, among other more consistant things, these sequences, you will receive a copy. Best Regards, Melvyn. ______________________________________________________________________________ Melvyn Jeremie Lafitte | Departement de Mathematiques dit Mandelvyn | Ecole Polytechnique Federale de Lausanne Email: melvyn.lafitte@dma.epfl.ch | ETH-Lausanne (Sister of ETH-Zurich) ______________________________________________________________________________ "If you really believe in quantum mechanics, then you can't take it seriously." Bob Wald. ______________________________________________________________________________ From njas Tue Aug 29 21:27 EDT 1995 Received: by rice; Tue Aug 29 21:27 EDT 1995 From: research!njas Date: Tue, 29 Aug 95 21:27 EDT To: masg32.epfl.ch!lafitte Cc: njas@research.att.com thank you for the message and the compressed file i added the extra terms ( and made that correction) to the second sequence to save time, could you simply send me the third sequence, the new on, in my standard format? following the example of tyhe second sequence, which now reads: %I A0361 %S A0361 1,0,2,1,1,2,5,0,10,6,3,2,19,2,10,1,5,10,89,1,170,28,7,2,71,12 %T A0361 170,5,25,10,21,0,42,26,51,10,1251,38,682,6,301,170,5833,3,2730 %U A0361 120,15,2,271,56 %N A0361 From a self-replicating tiling. %R A0361 %K A0361 nonn %O A0361 0,3 %E A0361 corrected 8/95. %A A0361 Melvyn Jeremie Lafitte then i will be very happy to add it to the table! best regards neil From masg49.epfl.ch!lafitte Wed Aug 30 11:44:09 0600 1995 Received: by rice; Wed Aug 30 05:45 EDT 1995 Received: by research.att.com; Wed Aug 30 05:44 EDT 1995 Received: from masg49.epfl.ch by sicmail.epfl.ch with SMTP (PP) id <20772-0@sicmail.epfl.ch>; Wed, 30 Aug 1995 11:44:09 +0200 From: Melvyn Lafitte Message-Id: <9508301144.ZM7113@dma.epfl.ch> Date: Wed, 30 Aug 1995 11:44:09 -0600 In-Reply-To: njas@research.att.com "" (Aug 29, 9:27pm) References: <199508300128.DAA09102@masg32.epfl.ch> X-Mailer: Z-Mail (3.2.0 26oct94 MediaMail) To: njas@research.att.com Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Status: RO Attn: NJA Sloane Thank you for the message. Here is the 3rd sequence in your standard format: %I A0362 %S A0362 1,1,0,0,3,3,0,0,1,0,1,1,2,0,7,7,0,2,1,1,0,1,2,2,3,0,3,6,10 %T A0362 0,13,2,9,3,10,0,15,15,0,10,3,9,2,13,0,10,6,3,0,3,2,2,5,2,25 %U A0362 1,42,12,7,0,7,28,170,1,217,10,37,1 %N A0362 From a self-replicating tiling. %R A0362 %K A0362 nonn %O A0362 0,5 %A A0362 Melvyn Jeremie Lafitte I did not know what to write at the A???? place, so i've just put A0362. When i'll have more time for this, i will devise a (very ?) short Mathematica program, out of the ones i use now, to calculate this 3rd sequence and will send it to you. Best Regards, Melvyn. ______________________________________________________________________________ Melvyn Jeremie Lafitte | Departement de Mathematiques dit Mandelvyn | Ecole Polytechnique Federale de Lausanne Email: melvyn.lafitte@dma.epfl.ch | ETH-Lausanne (Sister of ETH-Zurich) ______________________________________________________________________________ Rabbi Zoucha d'Anipoly avait pour habitude de repeter: "Zoucha, Quand tu retourneras chez ton Cre-teur, Il ne te demandera pas pourquoi tu n'etais pas Moise ou David mais pourquoi tu n'etais pas Zoucha ! " ______________________________________________________________________________ From njas Wed Dec 13 07:37 EST 1995 To: melvyn.lafitte@dma.epfl.ch, njas@research.att.com Hi! i now have a home page, with a section on Integer Sequences that you might find interesting! i an adding links to the sequence table - is there a URL address for any of the sequences you sent me, such as this one? %I A0876 %S A0876 1,1,0,0,3,3,0,0,1,0,1,1,2,0,7,7,0,2,1,1,0,1,2,2,3,0,3,6,10, %T A0876 0,13,2,9,3,10,0,15,15,0,10,3,9,2,13,0,10,6,3,0,3,2,2,5,2,25, %U A0876 1,42,12,7,0,7,28,170,1,217,10,37,1 %N A0876 From a self-replicating tiling. %R A0876 %K A0876 nonn %O A0876 0,5 %A A0876 Melvyn Jeremie Lafitte [melvyn.lafitte@dma.epfl.ch] best regards Neil Sloane, njas@research.att.com, fax: 908 582 2379 Bell Labs, Room 2C-376, 600 Mountain Ave, Murray Hill, NJ 07974 USA Home page: http://netlib.att.com/math/sloane/doc/home.html From melvlafitte@hotmail.com Sun Jul 1 14:18:23 2007 Received: from mail-gray.research.att.com (mail-gray.research.att.com [135.207.30.104]) by fry.research.att.com (SGI-8.12.5/8.8.7) with ESMTP id l61IINdS23524971 for ; Sun, 1 Jul 2007 14:18:23 -0400 (EDT) Received: by mail-gray.research.att.com (Postfix) id 3D1EE9E008E; Sun, 1 Jul 2007 14:18:22 -0400 (EDT) Delivered-To: njas@research.att.com Received: by mail-gray.research.att.com (Postfix, from userid 612) id 3BE179E008D; Sun, 1 Jul 2007 14:18:22 -0400 (EDT) X-Spam-Checker-Version: SpamAssassin 3.1.9 (2007-02-13) on mail-gray.research.att.com X-Spam-Level: * X-Spam-Status: No, score=1.3 required=4.0 tests=BAYES_40,HTML_40_50, HTML_MESSAGE,SUBJ_ALL_CAPS autolearn=no version=3.1.9 Received: from mail-dark.research.att.com (mail-dark.research.att.com [192.20.225.112]) by mail-gray.research.att.com (Postfix) with ESMTP id 792359E008E for ; Sun, 1 Jul 2007 14:18:04 -0400 (EDT) Received: from bay0-omc2-s27.bay0.hotmail.com (bay0-omc2-s27.bay0.hotmail.com [65.54.246.163]) by mail-dark.research.att.com (Postfix) with ESMTP id 5508511C333 for ; Sun, 1 Jul 2007 14:18:04 -0400 (EDT) Received: from BLU110-W7 ([10.6.61.42]) by bay0-omc2-s27.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.2668); Sun, 1 Jul 2007 11:18:03 -0700 Message-ID: Content-Type: multipart/alternative; boundary="_816574b1-2981-4768-bda2-61f04b6675b2_" X-Originating-IP: [82.248.35.67] From: =?iso-8859-1?Q?Melvyn_J=E9r=E9mie_Lafitte?= To: CC: Subject: A000360, A000361, A000876 Date: Sun, 1 Jul 2007 19:18:03 +0100 Importance: Normal MIME-Version: 1.0 X-OriginalArrivalTime: 01 Jul 2007 18:18:03.0895 (UTC) FILETIME=[2A515070:01C7BC0C] Status: RO --_816574b1-2981-4768-bda2-61f04b6675b2_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear NJAS,As the author of A000360, A000361, A000876, I would like to w= rite a long due paper on the fabric of these sequences, including geometric= al and topological matters related to the old work which led to these... I = guess that JIS is the right place to publish? May I ask you to change my "a= uthor email" to "mjlafitte(AT)gmail.com". The former address is rarely in u= se, correspondence on the latter is and will be dealt with.It's amazing how= in 12 years your encyclopedia has changed, it's really humongous now; fant= astic work! With best wishes,MJL _________________________________________________________________ Express yourself instantly with MSN Messenger! Download today it's FREE! http://messenger.msn.click-url.com/go/onm00200471ave/direct/01/= [JIS = Journal of Integer Sequences. No paper by him was ever published there. Whether a paper was submitted I do not know.]